Asynchronous binary counter circuits



March l, 1966 A, s, MERRIAM 3,238,461

ASYNCHRONOUS BINARY COUNTER CIRCUITS l Filed oct. 11, 1963 a/mM/w/mff @nl @u @la 1N VENTOR.

traf/rey United States Patent O 3,238,461 ASYNCHRONOUS BINARY COUNTER CIRCUITS Ann S. Merriam, Merion Station, Pa., assignor to Radio Corporation of America, a corporation of Delaware Filed Oct. 11, 1963, Ser. No. 315,629 6 Claims. (Cl. 328-41) This invention relates to new and improved binary counter circuits.

The circuits of the invention are useful in asynchronous data processing machines. Asynchronism implies that each operation in a group of sequential operations performed by the machine occurs in response to a signal indicative of the completion of the preceding operation. The time required to complete each operation may be variable. This contrasts with synchronous data processing machine operation, wherein each operation is performed in response to (in synchronism with) a clock pulse, and the clock pulses occur during xed, regularly spaced time intervals.

In the circuits of the invention, each stage of the counter includes a pulse producing circuit. Each such circuit produces an output pulse in response to a change, in a given sense, of the storage state of its stage. For eX- ample, each pulse producing circuit may be connected to produce an output in response to the -1 transistion of its counter stage. In addition, the last (the highest order) counter stage includes a circuit for producing an output pulse in response to a change in the opposite sense (a 1-0 transition in this example) in the storage state of the last counter stage. A circuit which is common to all of the pulse producing circuits produces a carry propagation complete pulse, in response to each input pulse to the counter, only after a period which is a function of the time, in each case, for the counter to settle down to its new count.

The invention is discussed in greater detail below and is illustrated in the following drawings of which:

FIGS. la through le are schematic drawings of the conventions employed in FIGS. 2 and 3;

FIG. 2 is a block circuit diagram of one embodiment of a counter according to the invention; and

FIG. 3 is a block circuit diagram of a second embodiment of a counter according to the invention.

FIGS. la-le are more or less self-explanatory. The convention arbitrarily adopted, for purposes of the pressent explanation, is that a binary 0 is represented by a relatively low value of voltage and a binary 1 is represented by a relatively high value of voltage. Thus, in FIG. 1a when the input voltage applied to the trigger (T) terminal changes from a low level to a high level (from a O to a 1), the flip-flop changes its storage state.

The three logic gates shown in FIGS. 1b, c and d are NOR, AND and OR gates respectively, and their operation is succinctly given by the Boolean equations appearing next to the respective gates. These gates and the nip-flops receive inputs and produce outputs which represent binary digits (bits). For the sake of convenience, such inputs are sometimes referred to in the discussion which follows as 1s or 0s rather than as signals, voltages or levels manifesting such bits.

The counter of FIG. 2 includes three triggerable flipops 10, 12 and 14, respectively. Input timing pulses (TP) are applied to the trigger terminal 16 of the lowest order flip-Hop 10. The unbarred output terminal of flipop is connected to the trigger input terminal T of ip-op 12 and the unbarred output terminal of Hip-flop 12 is connected to the trigger input terminal T of ilipiiop 14.

The barred output terminals of the respective tlip-ops are connected through delay lines 18, 18a and 18b, re-

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spectively, to one input terminal of NOR gates 20, 20a and 20h, respectively. The unbarred output terminals of the respective ip-ops are directly connected, via leads 22, 22a and 22b, respectively, to the second input terminal of the respective NOR gates. The dip-flop 14, which stores the -bit of highest rank, is connected at its unbarred output terminal through a delay line 24 to an input terminal of NOR gate 26. The barred output terminal of ip-op 14 is directly connected via lead 28 to the second input to NOR gate 26. All of the NOR gates are connected to a common OR gate 30. This OR gate produces a carry propagation complete signal H,'as is discussed shortly.

In the operation of the circuit of FIG. 2, all of the Hip-flops are initially in their 0 storage state. In other words, each ip-op initially produces a low voltage level (binary 0) at .its barred output terminal and a high voltage level (binary 1) as its unbarred output terminal. A 0 is therefore initially present at input lead 32 to NOR gate 20 and a 1 is initially present at input lead 34 to NOR gate 20. Accordingly, this NOR gate is initially disabled.

When the first timing pulse TP-I is applied to input terminal 16, a iiip-op 10 changes its storage state. In other words changes to 1 and A changes to 0. The A=0 is applied immediately to NOR gate 20. However, the =1 does not reach NOR gate 2t) until after the time delay A! inserted by delay line 18. Therefore, during the interval At after the Hip-flop 10 switches from its 0 to its 1 state, both input leads 32 and 34 of the NOR gate 20 carry a 0, whereby the NOR gate is enabled and produces a D21 output. Upon the completion of the delay interval At, the bit present at input lead 32 of the NOR gates changes from a 0 to 1 inactivating the NOR gate whereby D becomes 0.

The D=1 output of NOR gate 20 is applied to OR gate 30 which thereupon produces an H =1 output. H :1 is a carry propagation complete pulse. This pulse indicates that the timing pulse TP applied to the counter has completed incrementing the count stored in the counter by 1. In other words, no carry will propagate after H =1 occurs, until the next timing pulse is applied to terminal 16. In the present example of a change in the count from 000 to 001, the time required after the application of TP-1 for H to become equal to 1, is the time necessary for the rst stage, iiip-op 10, to switch from its 0 to its 1 state. The H=1 signal indicates to the data processing machine of which the counter of FIG. 2 may be a part that the counter has settled to its new count and that the next operation the machine is to perform involving the counter can commence.

In response to the second timing pulse TP-2 applied to input terminal 16 flip-nop 10 changes from the 1 back to the 0 storage state. The NOR gate 20 is not enabled by a 1-0 transition of flip-flop 10 so that D remains 0. However, the 1-0 transition of flip-nop 10 corresponds to a change in the unbarred output of the flipop from A=0 to A= 1. This transition is a triggering impulse for flip-flop 12 and, in response thereto, flip-dop 12 changes from the 0 to the 1 storage state. The second pulse producing circuit, consisting of delay line 18a, NOR gate 20a, and direct connection 22a thereupon produces an output E=1. E serves as an input to OR gate 30 so that when E changes to 1, H, the carry propagation complete pulse, also changes to 1.

The timing pulse TP-2 causes the count recorded in the counter to -change from 001 to 010. The time required for the counter to settle to the new count is two counter stage delays. The input triggering pulse causes flip-nop 10 to change its state. This is the trst stage delay. The change in state of ilip-iiop 10 causes Hip-flop 12 to 3. change its state. This is the second stage delay. The pulse H =l starts after these two stage delays and again indicates that the counter has settled to its new count. The table below illustrates the remainder of the opera tion of the circuit of FIG, 2. Each time a pulse D, E, F or G is generated, the carry -propagation complete pulse H occurs. It is clear from the table that the time at which H occurs is a function of the number of stage delays required for the counter to settle.

Flip-Flop Storage Output of Gates in Number of State Timing Response to T.I". Flip-Flop pulse Stage Delays Required tor C B A G F E D Counter to Settle 0 0 0 0 1 TP-l 0 0 O 1 1 U 1 0 'TP-2 0 0 1 0 2 0 1 1 'FP-3 0 O 0 1 1 1 0 0 TP-4 0 1 0 0 3 1 0 1 TP-5 0 0 0 1 1 1 1 0 IP- 0 0 1 0 2 1 1 1 TP-7 0 0 0 1 1 0 0 0 TP-S 1 0 O 0 3 The last counter stage 14 requires 2 pulse producing circuits. The circuit 18b, 201:, 22b produces an F=1 output in response to the 0-1 transition of ilip-iiop 14. This occurs in response to timing pulse TP-4 after three stage delays. The pulse producing circuit 24, 28, 26 produces an output pulse G=1 in response to the 1-0 transition of flip-flop 14. It occurs in response to the eighth timing pulse TP-8, which resets the counter to its original condition-storing 000. G=l occurs after three stage delays. The G=1 output may properly be termed an overflow indication.

In a modified form of the circuit of FIG. 2 an AND gate 40, connected as shown, replaces the NOR gate 27 and the delay line 24. The output pulse G produced by this gate is in response to a 1-0 transition of flip-op 14 and may be applied to OR gate 30. An advantage of this arrangement is that there is a saving of one delay line.

An important advantage of the circuit of FIG. 2 (and also of the circuit of FIG. 3) over synchronous binary counters is the saving in time which is made lpossible. In a synchronous counter, it is always necessary to wait an amount of time, after a triggering pulse is applied to the counter and before the next operation can start, which is equal to the longest possible time it may take the counter to settle down (the worst case condition). In the case of a three-stage counter such as described, it would be necessary, in each case, to wait three stage delays (plus a small amount of additional time, as a safety factor). In the present asynchronous counter, the next operation can start, in each case, immediately after the counter settles. The average settle down time is 1% stage delays. As the size of the counter increases the proportional saving in time increases. For example, a fourstage asynchronous counter according to the invention settles down, on the average, in 17s stage delays, compared to the worst case condition of four stage delays. A fifty-six stage asynchronous counter settles down, on the average, in approximately 2 stage delays, compared to the worst case condition of titty-six stage delays.

The embodiment of the invention shown in FIG. 3 is analogous to the one of FIG. 2 and similar reference numerals primed are applied to identify similar circuit elements. The circuit of FIG. 3 employs AND gates rather than NOR gates. It is therefore necessary, using the conventions given, to connect the AND gates directly to the barred terminals of the liip-liops and through the delay lines to the unbarred terminals of the flip-flops.

In the operation of the circuit of FIG. 3, the counter initially stores the count 000. The output of tiip-iiop TP-l occurs, changes to l and A changes to 0. 171:1

4 reaches the AND gate 20 immediately. But, A=0 does not reach the AND gate until after the time delay At' inserted by the delay line 18. Therefore, during the interval At', the two inputs to AND gate 20' are l, the AND gate becomes enabled, and the output D=l is produced. The D=1 applied to OR gate 30 causes the OR gate to -produce the carry propagation completed pulse H=1. After the interval At', the bit on lead 34 changes to 0 whereupon the AND gate becomes disabled and both D and H change back to 0.

The remainder of the operation of the circuit of FIG. 3 easily may be followed from the explanation of FIG. 2 above. The table above applies both to FIGS. 3 and 2..

While not critical, it is usual that all of the delay lines in a counter such as described insert substantially the same delay. This delay can be relatively short, if desired. The delay interval, in each case, will depend upon the pulse duration desired for H.

The invention has been illustrated in terms of three stage counters to simplify the explanations.

It is also to be understood that, in the circuit of FIG. 3, a NOR gate 1-0 transition pulse producing -circuit may be substituted for the AND gate pulse lproducing circuit 24 26 28', in a manner analogous to that shown in FIG. 3 for the substitution of the AND gate 40 for the.

NOR gate circuit 26, 24, 2S.

What is claimed is: 1. In combination,

a multiple stage counter, each such stage being capable of assuming either one of a zero and a one state;

a plurality of means, one per stage, each means for generating an output in response to a zero to one transistion of its stage;

another means, this one coupled to the stage of the counter representing the binary digit of highest rank, for generating an output in response to a one to zero transition of the stage representing the bit of highest rank; and

a circuit coupled to all of said means, for producing an output in response to an output from any of said means.

2. In combination,

a multiple stage, triggerable iiip-op counter, each tiipflop of said counter having a first and a second output terminal, one terminal for producing an output indicative of a digit and the other terminal for producing an output indicative of the complement of the binary digit;

a plurality of delay means, one for each flip-flop;

a plurality of two input coincidence gates, one for each flip-iiop, one input of each gate being connected directly to the first output terminal of its flip-flop, and the other input of each gate being connected through a delay means to the second output terminal of its flip-flop;

and an OR gate connected to receive the outputs of4 the respective coincidence gates.

3. In combination,

a multiple stage, triggerable flip-flop counter, each fliptiop of said counter having a iirst and a second output terminal, one terminal for producing an output indicative of a binary digit and the other terminal for producing an output indicative of the complement of the binary digit;

a plurality of delay means;

a plurality of two input coincidence gates, one for each counter, each for producing an output in response to a change in flip-flop stage in the same sense, one input of each gate being connected directly to the tirst output terminal of its iiip-iiop, and the other input of each gate being connected through a delay means to the second output terminal of its flip-flop;

an additional two input coincidence gate, this one for It is to 'bev understood, of course, that the invention is equally ap-4 plicable to counters of any number (such as n) of stages..

producing an output in response to a change in the state of its ip-op in the opposite sense, one input of said additional gate being connected directly to one of the output terminals of the flip-liep storing the binary digit of highest rank, and the other input of said additional gate being connected through one of said delay means to the other output terminal of the same flip-flop;

and an OR gate connected to receive the outputs of the respective coincidence gates.

4. The combination set forth in claim 3 wherein all of said coincidence gates are NOR gates.

5. The combination set forth in claim 3 wherein all of said coincidence gates are AND gates.

6. A binary counter comprising,

a plurality of triggerable ip-ops, each representing a binary digit of different rank, each except the ip-op representing the bit of lowest rank changing its storage state in response to a change in a given sense of the storage state of the immediately preceding flip-flop, and said flip-flop representing the binary digit of lowest rank being receptive of input trigger pulses, and changing its state in response to each said pulse;

a plurality of pulse producing circuits, one per ip-op, each for producing an output pulse in response to a change in said given sense of the storage state of its Hip-flop;

a pulse producing circuit coupled to the lone of said flop-flops representing the bit of highest rank for producing an output pulse in response to a change in an opposite sense of the storage state of said lastmentioned flip-Hop; and a circuit common to all of said pulse producing circuits for producing an output each time one of said pulse producinu circuits produces a pulse.

References Cited by the Examiner UNITED STATES PATENTS 3,028,552 4/1962 Hahs 328-55 3,107,332 10/1963 Paoletti et al 328-63 ARTHUR GAUSS, Primary Examiner. 

1. IN COMBINATION, A MULTIPLE STAGE COUNTER, EACH SUCH STAGE BEING CAPABLE OF ASSUMING EITHER ONE OF A "ZERO" AND A "ONE" STATE; A PLURALITY OF MEANS, ONE PER STAGE, EACH MEANS FOR GENERATING AN OUTPUT IN RESPONSE TO A "ZERO" TO "ONE" TRANSISTION OF ITS STAGE; ANOTHER MEANS, THIS ONE COUPLED TO THE STAGE OF THE COUNTER REPRESENTING THE BINARY DIGIT OF HIGHEST RANK, FOR GENERATING AN OUTPUT IN RESPONSE TO A "ONE" TO "ZERO" TRANSITION OF THE STAGE REPRESENTING THE BIT OF HIGHEST RANK; AND A CIRCUIT COUPLED TO ALL OF SAID MEANS, FOR PRODUCING AN OUTPUT IN RESPONSE TO AN OUTPUT FROM ANY OF SAID MEANS. 